To exit a room, you must open eight doors, that are initially closed. There are nine orbs that act on the doors, as follows:

Orb 1: Toggle door 1 (that is, close it if open, or open it if closed), open door 3 (if already open, leave it that way), and close door 5 (if already closed, leave it that way)
Orb 2: Open 3, close 4, open 7
Orb 3: Toggle 3, close 7, open 8
Orb 4: Open 1, open 3, toggle 5
Orb 5: Close 1, open 4
Orb 6: Toggle 2, open 3, close 5, open 6
Orb 7: Toggle 4 and 5
Orb 8: Open 3, close 7
Orb 9: Close 8

What is the shortest sequence of orbs you must touch in order to get all doors open?